To determine which dataset is more spread out, we can compare their mean absolute deviations (MADs):
- Dataset #1 has a mean absolute deviation of 48.2.
- We need to calculate the mean absolute deviation for Dataset #2: 401, 467, 489, 503, 568.
First, let's calculate the mean of Dataset #2:
\[ \text{Mean} = \frac{401 + 467 + 489 + 503 + 568}{5} = \frac{2428}{5} = 485.6 \]
Next, we calculate the absolute deviations from the mean for each value in Dataset #2:
- |401 - 485.6| = 84.6
- |467 - 485.6| = 18.6
- |489 - 485.6| = 3.4
- |503 - 485.6| = 17.4
- |568 - 485.6| = 82.4
Now, let's calculate the mean absolute deviation for Dataset #2:
\[ \text{MAD} = \frac{84.6 + 18.6 + 3.4 + 17.4 + 82.4}{5} = \frac{206.4}{5} = 41.28 \]
Now we can compare the MADs:
- Dataset #1: 48.2
- Dataset #2: 41.28
Since 48.2 (Dataset #1) is greater than 41.28 (Dataset #2), we can conclude:
Dataset #1 is more spread out than Dataset #2.
Thus, the correct response is:
"Dataset #1 is more spread out because it has a mean absolute deviation of 48.2 whereas Dataset #2 has a mean absolute deviation of 41.28."